CHANDRA HIGH-ENERGY GRATING OBSERVATIONS OF THE Fe Kα LINE CORE IN TYPE II SEYFERT GALAXIES: A COMPARISON WITH TYPE I NUCLEI

Figure 1 shows the HEG spectrum for each source in the Fe K region, corrected for instrumental efficiency and cosmological redshift. The spectra are binned at 0.01 Å, similar to the HEG FWHM spectral resolution of 0.012 Å. The statistical uncertainties correspond to 68% confidence Poisson errors, which we calculated using Equations (7) and (14) in Gehrels (1986) that approximate the upper and lower errors, respectively. For sources which were observed more than once, the time-averaged spectra are shown. It can be seen that in some spectra, emission lines from different ionized species of Fe are evident, in addition to the narrow Fe Kα line at ∼6.4 keV, but the latter is always the strongest line. Although in the present paper we are concerned only with the Fe Kα line core centered at ∼6.4 keV, overlaid on the spectra in Figure 1 are vertical dashed lines marking the expected positions of the Fe xxv He-like triplet lines (the two intercombination lines are shown separately), Fe xxvi Lyα, Fe i Kβ, and the neutral Fe K-shell threshold absorption-edge energy. The values adopted for these energies were from NIST2 (He-like triplet), Pike et al. 1996 (Fe xxvi Lyα), Palmeri et al. 2003 (Fe i Kβ), and Verner et al. 1996 (Fe K edge). We emphasize that the emission from higher ionization states of Fe has little effect on the measurements of the intrinsic width of the Fe Kα line. For example, for NGC 1068 the spectral plot in the Fe K band shows a broad emission feature on the blue side of the Fe Kα line peak, which is probably due to multiple species of ionic Fe. The occurrence of highly ionized Fe emission lines in AGN X-ray spectra has been noted since the ASCA observations, and they were extensively studied recently with XMM-Newton and Suzaku (e.g., Bianchi et al. 2005; Fukazawa et al. 2011). However, we can confirm from the 99% confidence contour of Fe Kα line intensity versus FWHM (Figure 2) that the Fe Kα line width is still well constrained (less than ∼3500 km s⁻¹). This conclusion is also consistent with the physical width of the narrow core of the Fe Kα line in the spectral plot that is apparent simply from visual inspection.

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The best-fitting Fe Kα emission-line parameters for each spectrum are shown in Table 2. We do not give the best-fitting values of Γ or N_H in Table 2 because the values derived using the simplistic continuum model are not physically meaningful but are simply parameterizations. We obtained a weighted mean line-center energy of 6.397 ± 0.001 keV for the 24 observations of eight sources. At 99% confidence (for three free parameters), none of the AGNs has a line centroid energy greater than ∼6.41 keV, indicating that the line-emitting matter is cold and essentially neutral, consistent with results presented in Paper I for a sample of type I AGNs. Here, and hereafter, for the calculation of the weighted mean of any quantity with asymmetric errors, we simply assumed symmetric errors, using the largest 68% confidence error from spectral fitting.

Table 2. Parameters of the Core Fe Kα Line Emission from $\it Chandra$ (HEG) Data

Source	F2–10 keV	E	EW	FWHM (Fe Kα)	I (Fe Kα)	L (Fe Kα)	FWHM (Hβ)	MBH	$L_{\rm [O\,\mathsc{iv}]}$
		(keV)	(eV)	(km s−1)			(km s−1)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
NGC 4945(2)⋆	2.6	6.389+0.007− 0.008	840+164− 191	2780+1110− 740	2.6+0.5− 0.6	39.31+0.08− 0.11	...	6.2	39.37
Circinus(4)⋆	16.0	6.396+0.002− 0.001	1673+91− 83	1710+190− 170	35.4+1.9− 1.8	40.22+0.02− 0.02	3300 †	6.1	40.50
NGC 6240(2)⋆	2.9	6.394+0.009− 0.009	333+96− 79	2810+1240− 880	1.2+0.3− 0.3	41.20+0.10− 0.12	...	9.0	41.82
NGC 1068(10)⋆	5.6	6.402+0.003− 0.003	779+72− 76	2660+410− 440	5.2+0.5− 0.5	40.23+0.04− 0.04	3030	7.2	41.78
Mrk 3⋆	6.3	6.396+0.007− 0.008	612+123− 104	3140+870− 660	7.7+1.5− 1.3	41.50+0.08− 0.08	6000	8.6	41.97
NGC 4507	27.9	6.395+0.007− 0.006	114+21− 26	2200+910− 720	11.0+2.0− 2.5	41.53+0.07− 0.11	5000 †	7.6	41.01
Centarus A(2)	310.8	6.396+0.005− 0.007	45+9− 8	2320+950− 650	26.4+5.2− 5.0	40.30+0.08− 0.09	...	8.3	39.86
NGC 4388(2)	23.1	6.393+0.004− 0.004	169+24− 21	2430+620− 590	10.0+1.4− 1.2	41.16+0.06− 0.06	3100	7.2	41.61
NGC 4258(3)	9.0	6.4 (fixed)	14+9− 9	100 (fixed)	0.2+0.1− 0.1	37.96+0.18− 0.30	...	7.6	38.57
NGC 1275(2)	30.2	6.4 (fixed)	19+14− 15	100 (fixed)	0.6+0.4− 0.4	40.63+0.22− 0.48	...	8.5	40.74

Notes. Results from Chandra HEG data, fitted with a absorbed power law plus Gaussian emission-line model in the 3–10 keV band. All parameters are quoted in the source rest frame. Statistical errors are for the 68% confidence level for three free parameters in the Gaussian component of the model (corresponding to ΔC = 3.506). For NGC 4258 and NGC 1275, the 1σ statistical errors are for one free parameter, corresponding to ΔC = 0.989. Column 1: source name, while parentheses show the number of the observations used to produce the time-averaged spectrum. All HEG observations were in the Chandra public archives as of 2010 Aug 1 (see Section 2). ^⋆Compton-thick AGN; Column 2: the observed 2–10 keV flux in units of 10⁻¹² erg cm⁻² s⁻¹; Column 3: Gaussian line centroid energy; Column 4: emission-line equivalent width; Column 5: full width at half-maximum of the Fe Kα, rounded to 10 km s⁻¹. Column 6: emission-line intensity in units of 10⁻⁵ photons cm⁻² s⁻¹. Column 7: the logarithm of Fe Kα line luminosity in units of erg s⁻¹; Column 8: full width at half-maximum of the broad polarized Hβ line, refers to Oliva et al. 1998; Nishiura & Taniguchi 1998; Moran et al. 2000; Young et al. 1996. † Broad polarized Hα line. Column 9: black hole mass, refers to: Greenhill et al. (1997); Bian & Gu (2007); Tecza et al. (2000); Tremaine et al. (2002); Marconi et al. (2001); Woo & Urry (2002). Column 10: logarithm of the [O iv] emission-line luminosity, refers to: Liu & Wang (2010); Meléndez et al. (2008b).

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From our spectral fits (Table 2) and the joint confidence contours of Fe Kα line intensity versus FWHM (Figures 2 and 3), we found that at 99% confidence, the Chandra HEG resolves the narrow component of the Fe Kα emission in 8 out of 10 sources. The weighted mean FWHM of the Fe Kα line cores is 2000 ± 160 km s⁻¹. The fact that this mean is approximately equal to the HEG FWHM spectral resolution is not indicative of a calibration bias. This is supported by the fact that the FWHM of the Fe Kα line in Circinus is less than the HEG FWHM at a confidence level of greater than 99%. In addition, the spectral resolution for gratings does not degrade with time because it is determined principally by spatial dispersion, and the resolution is well established from bright Galactic sources with narrow lines (http://space.mit.edu/CXC/calib/hetgcal.html). Note that the weighted mean value is consistent with the straight mean of the FWHM, of 2510 ± 160 km s⁻¹.

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The measurements of the intrinsic width of the line can potentially be used to constrain the location of the medium responsible for the core of the Fe Kα emission line (e.g., Yaqoob et al. 2001). Comparing the Fe Kα line FWHM with that of the optical broad emission lines (e.g., Hα and/or H_β  lines) can give a direct indication of the location of the Fe Kα line-emitting region relative to the optical BLR (Nandra 2006; Bianchi et al. 2008; Paper I). To place limits on the location of the Fe Kα emitter relative to the BLR, we compiled from the literature the width of optical broad emission line from spectropolarimetric observations for five sources in our sample, and the values of the Hα or H_β FWHM⁴ are listed in Table 2. The near-infrared broad lines have not been taken into account in the present paper, as they are possibly produced in a region that differs from the BLR in density, and/or in the amount of extinction (e.g., Ramos Almeida et al. 2008; Landt et al. 2008). However, in cases where there is no spectropolarimetric data at all, the FWHM of near-infrared lines might still yield some useful information.⁵

Figure 3 shows the 99% confidence contours of the Fe Kα line intensity versus the ratio of the Fe Kα FWHM to optical line FWHM. We found that at the two-parameter 99% confidence level, the FWHM ratio lies in the range of ∼0.3–1.2. At 99% confidence, the Fe Kα line widths in three out of five sources are less than that of optical lines, suggesting that the observed Fe Kα emission is not likely produced in a BLR where the optical lines are produced. The remaining two sources (NGC 4388 and NGC 1068) could have consistent width for both lines. This would be expected in at least one source, NGC 4388, which is known to have significant column density variations (Elvis et al. 2004), if its BLR acts as absorber and emitter seen in the X-ray band. In fact, there is now significant evidence that the BLR may act as an X-ray absorber, as in the cases of NGC 1365 and NGC 7582 (e.g., Risaliti et al. 2005; Bianchi et al. 2009). However, if the BLR is obscured by a fully covering column density greater than ∼5 × 10²³ cm⁻² (as in the cases of NGC 4507, Mrk 3, and the Circinus) any Fe Kα line component from the BLR will be greatly diminished or undetectable. If the BLR is obscured by such a large column density, the only way it would be possible to observe an Fe Kα line component from the BLR is if the BLR is not fully covered. The fact that the Fe Kα line width of Compton-thick source NGC 1068 is consistent with that of the polarized H_β  line (within 99% errors) could be simply attributed to the large error in the Fe Kα line width. Alternatively, this could indicate that the heavy obscuration which blocks the BLR has comparable size with that of the BLR.

Since Keplerian velocities are inversely proportional to the square root of the orbit size, the observed distribution of the ratio of the Fe Kα to optical line FWHM implies that the Fe Kα line-emitting region size could be a factor of ∼0.7–11 times larger than the optical line-emitting region. We obtained a weighted mean of 0.57 ± 0.05 for the ratios of the Fe Kα line FWHM to the optical line FWHM, corresponding to the Fe Kα line-emitting region being, on average, ∼3 times the size of BLR. However, for AGNs in general, there may be no universal location of the Fe Kα line-emitting region within a factor of ∼1–10 times size of BLR. However, as we will show later, the Fe Kα line emitter may be associated with a universal location in terms of gravitational radius (r_g, where r_g = GM_BH/c²). If the Fe Kα line emission has a significant contribution from the putative obscuring torus that is required by AGN unification models, our results show that the size scale of the torus may be smaller than traditionally thought. Note that Gaskell et al. (2008) argue that there is considerable observational evidence that the BLR itself has a toroidal structure and that there may be no distinct boundary between the BLR and the classical parsec-scale torus.

One of the interesting things that we can investigate is whether the material responsible for producing the narrow Fe Kα line in type II AGNs systematically differs from that in type I objects. Of the AGNs in the sample reported in Paper I, we identified 13 type I AGNs (including three moderately obscured sources with weak broad Balmer lines, formally classified as intermediate-type AGNs) that provided the very best statistical constraints on the Fe Kα line FWHM (as indicated by the two-parameter confidence contours of line flux versus FWHM; see Figure 6 in Paper I). The weighted mean FWHM of the Fe Kα core is 2170 ± 220 km⁻¹, in good agreement with the measurement for type II AGNs in the present sample. However, we found a slightly larger FWHM of the Fe Kα line (3620 ± 220 km ⁻¹) for type I AGNs if the straight mean is used, but as we will show below, it may be due to a bias toward the measurements with lower quality data. We show in Figure 4 the distribution of Fe Kα line FWHM for the current sample (solid line), compared with the 13 type I AGNs in Paper I (dashed line). It can be seen that both histograms are not Gaussian and are not strongly peaked. In addition, we found that the measurement of the FWHM in one AGN (namely, MCG-6-30-15) deviated significantly from the distribution of the rest of the sources. From our empirical analysis, we obtained FWHM = 11880⁺⁴⁶⁵⁰_{− 4030} km s⁻¹ (see Paper I) for this object, and the corresponding 90% confidence lower limit (for three free parameters) is ∼6000 km s⁻¹. Note that MCG-6-30-15 has the strongest and broadest Fe Kα line yet observed in an AGN. The larger FWHM obtained from our empirical analysis could be attributed to the Fe Kα core from underlying disk-line component and/or a complex continuum (e.g., Miller et al. 2008). Note that Young et al. (2005) analyzed the Chandra HEG spectrum by using more complex models including both disk-line and narrow Fe Kα core emission, and obtained an FWHM < 4700 km s⁻¹ for the narrow component, which is consistent with those from the other sources in our sample. However, as the narrow Fe Kα line EW is relatively low (∼60 eV, see Paper I), we cannot tell whether the line profile is affected by the complex continuum or whether it is intrinsically broader than the other AGNs. Future X-ray missions, such as Astro–H, which has much higher spectral resolution, will help to measure the true profile of the narrow Fe Kα emission line in this object. Even considering the one AGN mentioned above, there is not a significant difference in the distribution of FWHM for the two subsamples. A Kolmogorov–Smirnov (K-S) test shows that the probability that the type I (including MCG-6-30-15) and type II AGNs are drawn from the same parent population is 0.83. Therefore, it appears that there is no difference in the origin of the Fe Kα line in type I and type II AGNs, which is consistent with the predictions of the unification model.

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Figure 5 shows the relationship between the Fe Kα line FWHM and the black hole mass (see caption of Table 2 for references). Open and solid circles denote type I and type II AGNs, respectively. We see that all FWHM values, within the statistical errors, are consistent with a constant, independent of the mass of black hole. Assuming that the line originates in material that is in a virialized orbit around the black hole, we can estimate the distance, r, of the line-emitting material to the black hole using the relation GM_BH = r〈v²〉. Assuming that the velocity dispersion is related to FWHM velocity as 〈v²〉 = $3\over 4$v²_FWHM (Netzer et al. 1990), we can obtain r = (4c²)/(3v²_FWHM)r_g, where r_g = GM/c². Using the weighted mean of FWHM ∼ 2000 km s⁻¹, we find that the r ∼ 3 × 10⁴r_g, larger than the typical size of the BLR (e.g., Peterson et al. 2004). Therefore, our results seem to support the bulk of the Fe Kα line production arising from a region that appears to be located at a universal distance with respect to the gravitational radius, which is controlled by central black hole mass. Note that Nandra (2006) also examined the relation between the FWHM of Fe Kα line and the black hole mass, but their results were ambiguous. The reason why they did not find the result that we found is possibly due to the fact that some of the sources in their sample had only poor quality and/or problematic Fe Kα line width measurements. Including such sources could have obscured the underlying result that r/r_g may be the key factor that determines the location of the line-emitting region. However, it is important to note that even with superb Chandra HEG spectral resolution, there may be blending from a Compton-shoulder component and/or multiple low ionization states of Fe (e.g., Yaqoob & Murphy 2011), so that the true line width may be less than the FWHM deduced from our simplistic model-fitting.

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From a theoretical point of view, the flux or luminosity of the Fe Kα line (L_Fe) is nontrivial to calculate, as it depends on a number of factors, including geometry, orientation, covering factor, element abundance, and column density of the line-emitting material. Using Monte Carlo simulations of a toroidal X-ray reprocessor model, Murphy & Yaqoob (2009, see also Yaqoob et al. 2010) showed that geometrical and inclination angle effects become important for N_H ≳ 10²³ cm⁻² for the observed EWs and line flux. For a given covering factor and set of element abundances, a toroidal structure with a column density of greater than ∼5 × 10²⁴ cm⁻², observed at an edge-on inclination could produce an Fe Kα emission line flux that is an order of magnitude or more weaker than a face-on orientation (Yaqoob et al. 2010). In particular, the Fe Kα line luminosity is not simply a linear function of N_H, and it has a maximum value for a column density in the range ∼3–8 × 10²³ cm⁻², depending on the inclination angle. Therefore, the Fe Kα line luminosity cannot be trivially used to measure the intrinsic AGN luminosity (L_AGN). The relation between L_Fe and L_AGN is more complicated than we would expect from optically thin matter, and it is strongly model dependent, and in particular it depends on covering factor, inclination angle, and column density. We emphasize that the column density for producing the Fe Kα line does not refer to the line-of-sight value, but rather to a value that corresponds to the angle-averaged flux over all incident X-ray continuum radiation (see Murphy & Yaqoob 2009).

Recently, Liu & Wang (2010) confirmed that L_Fe and L_AGN are not simply related. They compared the narrow Fe Kα line emission between type I and type II AGNs, using data obtained with XMM-Newton, and found that statistically, the Fe Kα line luminosities in Compton-thin and Compton-thick type II AGNs are about 2.7 and 5.6 times lower than that in type I sources, respectively. They therefore proposed that different correction factors should be applied if one uses the Fe Kα line emission to estimate the AGN's intrinsic luminosity. To examine the relation between L_Fe and L_AGN for our Chandra grating sample, we plot in Figure 6 (upper panel) the Fe Kα line luminosity (L_Fe) versus the [O iv] 25.89 μm line luminosity ($L_{\rm [\rm O\,\mathsc{iv}]}$, which is claimed to be an intrinsic AGN luminosity indicator, see Meléndez et al. 2008a). The type II AGNs are shown with solid circles, while open circles represent 24 type I AGNs for which the [O iv] line luminosity is available from literature. Solid stars denote tentative Compton-thick sources, based on previously reported measurements of N_H (e.g., Treister et al. 2009, and references therein). The right-hand panel shows the distribution of L_Fe for both type I (dotted line) and type II (solid line) AGNs. It can be seen that the distribution of the Fe Kα line luminosity in type II AGNs is not significantly different from that in type I AGNs. A K-S test shows the probability that both samples were drawn from the same parent population is 0.21. However, when normalizing the Fe Kα line luminosity by the [O iv] line luminosity (L_Fe/$L_{\rm [\rm O\,\mathsc{iv}]}$, the lower panel of Figure 6), we find a marginal difference in the distributions of the L_Fe/$L_{\rm [\rm O\,\mathsc{iv}]}$ ratio for type I and type II AGNs, but the significance level is not high (at 93% confidence), possibly due to the small size of the current Chandra grating sample. The dotted and dashed horizontal lines show the means of L_Fe/$L_{\rm [\rm O\,\mathsc{iv}]}$ for Liu & Wang's type I and type II subsamples, respectively. It seems that the distribution of the L_Fe/$L_{\rm [\rm O\,\mathsc{iv}]}$ ratio for our Chandra grating sample shows a similar pattern as Liu & Wang's sample. However, we note that there is significant overlap between the type I and type II AGNs with intermediate values of the L_Fe/$L_{\rm [\rm O\,\mathsc{iv}]}$ ratio (see also Liu & Wang 2010, Figure 6), suggesting the complex dependencies of the Fe Kα line emission on the geometry and physical properties of the line-emitting material. In the context of a toroidal geometry (e.g., Murphy & Yaqoob 2009), the sources in the overlap region of the L_Fe/$L_{\rm [\rm O\,\mathsc{iv}]}$ plot may however indicate that they constitute a selected distribution ofN_H and inclination angle (e.g., Circinus galaxy, Yang et al. 2009), but a larger sample is required to make a detailed comparison.

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Although in our study we cannot determine some of the critical parameters of the Fe Kα line emitter, such as global covering factor, N_H, and the inclination angle of the X-ray reprocessor, we can still make interesting statements from the plot of $L_{\rm [\rm O\,\mathsc{iv}]}$ versus L_Fe/$L_{\rm [\rm O\,\mathsc{iv}]}$. It is apparent that the ratio of L_Fe/$L_{\rm [\rm O\,\mathsc{iv}]}$ appears to have a dispersion of two to three orders of magnitude or so. Regardless of AGN type, the sources located at the top end of the L_Fe/$L_{\rm [\rm O\,\mathsc{iv}]}$ ratio distribution are expected to be those objects that are observed at a face-on, or near face-on, inclination angle, with moderate N_H (∼0.5–2 × 10²⁴ cm⁻²). The sources located in the region of the lowest values of L_Fe/$L_{\rm [\rm O\,\mathsc{iv}]}$ should correspond to cases with higher N_H and higher inclination angles. We note that the source with the lowest ratio of L_Fe/$L_{\rm [\rm O\,\mathsc{iv}]}$ is the prototypical type II Seyfert galaxy NGC 1068, for which an edge-on orientation of the torus and a high, Compton-thick column density has already been suggested in literature (e.g., Pounds & Vaughan 2006, and references therein).